The Islanders' Mathew Barzal celebrates his game-winning goal in overtime against the Devils...

The Islanders' Mathew Barzal celebrates his game-winning goal in overtime against the Devils Friday.  Credit: AP/Bill Kostroun

NEWARK — An inability to respond well to adversity had been one of the Islanders’ foremost problems of late. And the Devils kept testing them on Friday, tying the score three times, including late in regulation.

This time, the Islanders rose to the occasion.

“That kind of stuff happens and good teams respond,” Islanders center Mathew Barzal said. “We knew we wanted the extra point. We thought we deserved it right from the start and we’re glad to get it.”

Barzal, sprung by Brock Nelson, got ahead of defenseman Damon Severson for a partial breakaway in three-on-three play and scored the winner at 3:40 of overtime as the Islanders snapped a two-game losing streak with a 4-3 victory at Prudential Center.

“We weren’t happy with the last couple of games we played and we just needed a response,” added goalie Thomas Greiss, who made 39 saves for his second win over the Devils this season. “I think everybody chipped in today and it was a great effort.”

The Islanders (11-8-2), who will play the Hurricanes on Saturday night at Barclays Center, had allowed 16 goals in their previous three games and were coming off Wednesday’s 5-0 loss to the Rangers at Madison Square Garden.

The Islanders gave up three first-period goals in that game and four second-period goals in a 6-2 loss to the Stars in Brooklyn on Sunday, indicative of their problems putting together a full 60-minute effort.

The Islanders' Mathew Barzal  celebrates his game-winning goal in overtime...

The Islanders' Mathew Barzal  celebrates his game-winning goal in overtime against the Devils.  Credit: Getty Images/Elsa

So with Farmingville’s Keith Kinkaid (31 saves) off for an extra skater, Marcus Johansson’s goal with 10.2 seconds left in regulation might have been a crusher in another game.

“I liked our game a lot more,” Islanders coach Barry Trotz said. “There was more skin in the battle than we maybe had the last couple of games. We would have liked to get through the 60 minutes without giving up that late goal, but I liked our response. There was no sag. I’ve been complaining about sag after goals, and we didn’t have that today. We were hard and we were on the track of doing the things I liked.”

Jordan Eberle backhanded in his own rebound to make it 1-0 at 7:24 of the first period.  Taylor Hall fought his way to the crease and tied it at 1-1 at 11:48 of the second period. Greiss had stopped the first 56 shots he faced from the Devils this season, including a 35-save performance in a 3-0 win in Brooklyn on Nov. 3.

Anders Lee gave the Islanders a 2-1 lead at 14:14 of the second period as he established position at the right post.

Brian Boyle, with his 200th NHL point, tied it at 2 at 2:43 of the third. Boyle, who is in remission from chronic myeloid leukemia, scored on the Devils’ Hockey Fights Cancer day.

Defenseman Nick Leddy’s highlight-reel goal put the Islanders ahead 3-2 at 12:45 of the third period. He took the puck behind his crease, sidestepped Hall and completed an end-to-end rush by knocking in his own rebound.

“We did a lot of really good things throughout the game and we keep saying that, but we see how we have to play to be successful,” said Leddy, who scored his first goal of the season. “We stuck to our structure in overtime and Barzy had a great goal.”

The Devils (9-9-3) are among the NHL leaders with a home record of 7-1-3.

“That’s a good team over there. They’re going to get their chances,” Barzal said. “They’re going to put the puck in the net. I love the way we responded after every goal and never bent down.”

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